Friday, November 19, 2010

Eggertsson and Krugman

I was asked by a couple of readers to comment on this paper by Gauti Eggertsson and Paul Krugman. Krugman gives us the impression here that he is quite proud of this. We should certainly encourage Krugman if he wants to get back into the game. I would love to think that there is nothing holding back the senior members of the profession, and that we can learn new things, but when I can't remember what happened yesterday I have my doubts.

Eggertsson is a former Mike Woodford student, and a committed New Keynesian who works at the New York Fed (and appears to be visiting at Princeton, which explains the Krugman connection). He's supplying the New Keynesian technology to help Krugman to flesh out his thinking. The basic structure in the underlying model (some of which you need to go to the appendix to understand) is a standard New Keynesian framework. We have some infinite-lived optimizing consumers, and monopolistic competition. Some fraction of firms can set prices at will, and some must set prices one period ahead, i.e. there is time-dependent pricing. The nominal interest rate is set by the central bank according to a Taylor rule, and there is no money in the model (Woodford "cashless economy"), but of course goods prices are set in units of money.

The novelties here are the following. First, there is some heterogeneity among consumers, i.e. consumers can be one of two types, and types differ according to discount factors, so we have patient and impatient consumers. Second, there is an exogenous debt limit faced by each consumer, set in real terms. Third, debt is denominated in nominal terms, by assumption.

What we get from this is the following. Suppose the economy is in a steady state where the impatient consumers are borrowing from the patient ones, and impatient consumers are debt-constrained. Then, suppose that there is an exogenous shock to the debt limit. There is then a "deleveraging" effect. Debtors have to reduce their debts, and they do this by reducing consumption. The real interest rate falls, and could fall sufficiently that, in this sticky price framework, the nominal interest rate hits the zero lower bound. There is a further effect from debt deflation in that the price level falls, increasing the value of the debt, and requiring further deleveraging. Fiscal policy can have a big multiplier in these circumstances, in part for reasons Mike Woodford has studied, and in part because the debt constraint implies that Ricardian equivalence does not hold.

My comments are as follows:

In the introduction, the authors state:

Given both the prominence of debt in popular discussion of our current economic difficulties and the long tradition of invoking debt as a key factor in major economic contractions, one might have expected debt to be at the heart of most mainstream macroeconomic models– especially the analysis of monetary and fiscal policy. Perhaps somewhat surprisingly, however, it is quite common to abstract altogether from this feature of the economy1.

In the footnote they cite a few papers, including Bernanke and Gertler, Kiyotaki and Moore, and Gertler and Kiyotaki. It is certainly true that much of mainstream macroeconomics ignores the frictions that make credit, banking, and monetary exchange important. Indeed, this has been one of the key drawbacks of New Keynesian economics. Since the mid-1990s, Keynesian economists have focused their attention on sticky wages and prices, and have neglected other frictions, and the financial crisis made it clear that they had missed the boat. It's good that they are trying to make up for lost time now, but they have a lot to learn. Some neoclassicals were not any better at recognizing the importance of financial and monetary factors, for example the "Great Depressions of the 20th Century" volume gives short shrift to monetary and financial factors.

There is a lot of relevant work that Eggertsson and Krugman are unaware of, or are ignoring. Bruce Smith spent his career working on models of credit market frictions in monetary frameworks. I have work closely related to Bernanke-Gertler, and predating it (including my 1987 JPE paper). Many people have studied related debt-constrained problems. These include Kehoe and Levine (1993) and Kocherlakota (1996). There is a large literature that uses standard incomplete markets models (e.g. Aiyagari QJE 1993) to study problems associated with bankruptcy (e.g. this paper). New Monetarist Economics is all about monetary and financial frictions (see this).

In constructing and analyzing the model, the authors cut a lot of corners. First, the debt constraint is imposed exogenously. The authors are clearly aware that something deeper is required, but they don't seem to think this is a big problem. Second, the debt constraint is set in real terms, but for some reason (also not in the model) the debt contracts are nominal. Third, in analyzing the model, there is some linearization around a deterministic steady state, but the dynamics are not worked out from the model - these are essentially pseudo-dynamics.

Cutting corners matters. In particular, in environments where we are explicit about debt constraints, for example with explicit limited commitment, Ricardian equivalence can be hard to escape. For example, borrowers can face binding debt constraints in equilibrium, but if the government has no advantage over the private sector in collecting its debts, then the government is faced with the same problem in tax collection. If someone defaults on their private debts, they also default on their taxes. The economy will only be non-Ricardian if the government has some advantage in collecting on its debts. Maybe it does in practice, but it is important to model this so that we can understand it properly.

This is a kind of chicken model. We assume an advantage for the government in the credit market, in that the government can cut taxes today and increase taxes in the future, which effectively relaxes the credit constraints of borrowers, but only because the government can always collect the future taxes at no cost. This helps to give us big fiscal policy multipliers. In addition, there is some sleight-of-hand associated with an effect similar to what is in this paper by Woodford, where it is essentially monetary policy that is doing the work.

I can add to this my usual complaints about New Keynesian models. First, they are not explicit about monetary quantities and transactions, which are critical to how we need to think about monetary economies and monetary policy. This paper is more about fiscal policy, but the liquidity trap comes into play. If we want to understand that properly, we need a full-blown story about monetary frictions and central banking. Second, of course the constraints on pricing are exogenous. This obviously violates the Lucas critique. If pricing is so important, we need to think about how it responds to changes in policy rules. Third, Keynesian output effects are essentially by assumption. Firms have to, by assumption, supply whatever output is demanded at the price the firm is stuck with.

I think what the paper needs is the following:

1. Work out the results for the case with flexible prices. Indeed, one could start with a non-monetary economy. A basic Aiyagari incomplete-markets model will have the property that tightening up the borrowing constraint will lower the real rate, for example, but not much is known about dynamics. One could even compute solutions.

2. The linearization needs to be done for a fully-specified underlying stochastic model.

3. Where are those shocks coming from? It is not very informative to introduce a shock to the debt limit. The key thing is to understand how an increase in credit market frictions occurs as a result of factors that were occurring during the financial crisis.

4. The hard part is the debt-deflation story. In early versions of Bernanke-Gertler (1989), they tried to tell a debt-deflation story, but without success. The problem is that the best we have in terms of optimal contracting models are setups that deliver real debt contracts.

There are certainly some interesting ideas in here, but there are too many moving parts, and too many corners cut to feel very confident about the results the authors want to extract.

I guess much of the criticism about cutting corners applies to new keynesian models. There is a deep issue at stake which is, what do you say about policy when you don't know everything there is to know about how it affects the world? One answer is, you think harder until you know more The other is, you say something because time is passing and, under ignorance, doing nothing while you wait is as good or bad a choice as doing something. So you try to say the best you can given your time limit and your abilities.

Personally, I give Adam Smith his due: Division of labor is a wonderful thing. We are better off if there are people who are willing to cut corners in order to get to reasonable but shaky conclusions quickly as well as people who are willing to think deeply and slowly about the limits of these conclusions.

If we're going to assume some advantage for government, surely the ability to enforce contracts and raise taxes is a prime candidate?

As far as the debt novelty, I think that it's a pretty accurate representation of our current situation. Most contracts are in nominal terms, and most debt limits are for practical purposes in real terms. Krugman is simply trying to formalize a notion that's been around for a long time: the Keynes-Minsky debt-deflation spiral.

It would be great if Krugman provided a micro-founded theory for why there are nominal contracts at all and endogenized the debt limit, but he could argue that he's simply assuming the situation we see in the world and working out the macro consequences. I agree that we should take the policy recommendations with a grain of salt (Lucas critique), but I think that the dynamics of the system are quite interesting and informative.

"violate the lucas critique? but they have a lucas phillips curve? and rational expectations?"

The Lucas critique is just the idea that you want a model where the "sructure," i.e. decision rules followed by private agents, is invariant to changes in the policy rules under consideration. You can have Phillips curves and rational expectations and still violate the Lucas critique.

"There is a deep issue at stake which is, what do you say about policy when you don't know everything there is to know about how it affects the world?"

Yes, this is very important. Policy is made in real time, and we can't wait around for people to work out all the details before we start making decisions. There are questions about what corners to cut, how deep we should go, etc. In this case, we know enough to go deeper than these guys have on this particular problem.

"If we're going to assume some advantage for government, surely the ability to enforce contracts and raise taxes is a prime candidate?"

Exactly. The fiscal authority's role in the financial crisis has to come down to some advantage the government has as a creditor, and/or its coordinating role in sorting out complicated defaults. Similarly, if we're thinking about why QE2 might be useful, that has to have something to do with some advantage the Fed has as a financial intermediary.

Why do economists show such respect for Ricardian equivalence? Even Eggertsson and Krugman pay lip service to it, if only to argue it doesn't apply under certain conditions. The notion of immortal taxpayers who read the newspaper and correctly judge the future tax implications of everything they read there is obviously absurd. Look, people don't read the paper. To the extent they're at all aware of the budget deficit, they have no idea what the future tax implications are for them. They think tax cuts will unleash a flurry of creativity and productivity that will pay for themselves; or they think budget deficits will result in Weimar-style hyperinflation; or they're simply unaware of any of this because they're busy watching TMZ or running their business or raising their kids or whatever. And to the extent they judge the future tax implications of events in Washington, they fail to act on them. And no, if you sum up all the stupidity you don't get rational expectations, you just get summed up stupidity.

In any case, if by some miracle people on balance correctly judged the future tax implications of this year's stimulus spending, why would they save the total of it this year? It doesn't have to be paid back this year.

The paper makes a contribution to be sure (that sticky prices can interact with debt-deflation to drive interest rates to the zero bound, and fiscal policy can looses borrowing constraints), but it could be a lot better if it used modern techniques and built on some recent work rather than re-inventing (in a more-ad hoc fashion no less) the financial accelerator introduced by Kiyotaki, Moore, Bernanke and Gertler so long ago.

There is nothing new in the paper's debt constraint. Putting nominal values on one side and real on the other is not at all crucial to generating the debt-deflation phenomenon. Mendoza's sudden stop paper (AER forthcoming) and his paper on international financial crisis with Quadrini (JME 2010) have debt-deflation dynamics without stickiness or nominal prices at all. In addition, the AER paper (and to some extent the JME one) endogenously generate these dynamics in response to a real shock somewhere else in the economy rather than exogenously manipulating the constraint itself.

Further, I am deeply skeptical (and Steve seems to be as well) that linearization is an appropriate tool to study the model's dynamics. First-order approximations are very poor when the model is far from its steady state (exactly what happens in debt-deflation). Mendoza mentions this in his AER mentioned above, and he uses a global approximation method to deal with it. I think that's the only correct way to do it. In a model with heterogeneous agents this is especially true.

I second the last anonymous posters' puzzlement: Real households demonstrably do not make rational choices, and the financial system, which in principle, could correct the households' mistakes is arguably even worse.-brian

Well, perhaps attempting to measure, and then model, the degree to which actors are rational might be a somewhat less drastic solution. But suit yourself. The only thing I'd ask is if you construct models, and those models depend on assumptions that are patently false, that you refrain from making policy recommendations based on them. Or, like Cochrane, you can go ahead and make such recommendations, then act offended when people like Krugman ridicule you for it.

I always treat my students with respect. If you could see the look on my face when I say the words, you would get it. The point is that abandoning rationality is abandoning science - it leads nowhere. Model-building is an art. Any model we construct is going to be wrong, in some sense, and we have to be judicious about how we simplify and abstract from reality in order to create something useful. People behave in a predictable and organized fashion. Thus, it makes sense to represent how people behave in a model as being purposeful and rational. You can't measure rationality. It's not a testable hypoethesis. I can, however, construct models and test their predictions. You should not think that rationality somehow limits what you can put in a model - the possibilities are endless.

No, that's actually a giant logical leap, and is indeed characteristic of the political arguments on both sides of the spectrum. To counteract you example, how about going from "corruption is more prevalent in public rather than private spending" to "government is the root of all evil"?

But if you want to say you're scientific, then please be prepared to defend your models with logical arguments. I agree that the rational behavior hypothesis has some truth to it but in practice it violated so frequently that its predictions are close to useless.

"violate the lucas critique? but they have a lucas phillips curve? and rational expectations?"

The Lucas critique is just the idea that you want a model where the "sructure," i.e. decision rules followed by private agents, is invariant to changes in the policy rules under consideration. You can have Phillips curves and rational expectations and still violate the Lucas critique

.......

So here is how it looks to me.

In defining your Lucas critique, there it always applies. So in applying it to this paper you define it so broad that it is meaningless (after all, they use new classical phillips curve that Lucas used in his critique and rational expectations).

According your definition of Lucas critique it applies just as well to any model you write down with utility functions or production function, as, after all, we write them down to apply to describe particular behavior we observe which may be up to change (like the law of gravity).

In other words a meaningful statment of Lucas critique has to be made in some meaningful context, i.e. that it applies because of X,Y,Z, otherwise it is just an empty slogan like "being serious" about X,Y,Z. At the end of the day good theory is about making good assumption and being explicit about them. And criticism is most meaningful in the context of showing how and if those assumption is wrong (that why it also sound silly to talk about "non-linearities" as a catchphrase for some criticism without providing specific context. Sometimes non-linearities are important. Sometimes not.)

Certainly you can measure rationality. It's just hard. You examine situations in which changes in tax and spending policy have occurred and observe subsequent changes in savings by households. You're going to have limited data and it will be difficult to identify cause and effect and to separate any results you're looking for from exogenous causes. Yes, this is hard, and you may never find the relationships you're looking for. This means that you can't legitimately use such relationships in your models. I'm sorry. Rather than "the end of science", this is how science is done.

I believe Stephen's point is that the Calvo pricing violates the Lucas critique and he's quite corrrect in this.

The idea, as everyone from Calvo on has agreed, is just a tractable approximation for some sort of optimal behaviour. We don't really think something ever prevents price changes, just that agents, for a reason we haven't learned to model yet, choose to infrequeently adjust prices. So we model this behaviour by saying, in the model, that they "can't" change price anytime they want.

This violates the Lucas critique for I'd think a completely obvious reason, the observed behaviour that motivates the model was all during periods of relatively low inflation. Surely if inflation is higher then one of the reactions will be an increase in the frequency of price changes. In fact, wages being an important price, in the 70's in the UK skilled workers used to get quarterly cost of living adjustments instead of annual.

So, if you calibrate the model to have a certain parameter in the firm's pricing problem and then hold that parameter fixed in asking what happens if we increase inflation you get an answer that makes it seem like a great idea. But in real life you expect the parameter to change, invalidating your predicted outcome.

What if people are "irrational" in the sense that they have more pressing concerns than thinking about how debt affects them in the far future, whereas we, the economists,spend a lot of time thinking about it? Isn't the fact that the government is equipped with a large number of economists with PhD degrees that spent a large amount of time thinking about how the economy works and what happens in any given point in time an advantage? Perhaps we should be a bit more paternalistic?

I know this sounds outrageous, but it was Keynes's mindset and, except for our ideological sensibilities and a general sense that it is not good to be arrogant, it is not absurd on the face of it. In fact, you could argue that in the end of the day this is exactly how we think and how we behave. Why not be explicit about it in our models?

I'm trying to imagine what rationality would look like. Do you have, along with accounts for your kids' education and your retirement, a "future taxes" account? As a spending bill works its way through Congress, do you add more to this account when Congressman X expresses support for it, then decrease your contribution when Senator Y threatens to put a hold on the bill? Do you base your adjustment on CBO estimates, or does our rational actor figure the CBO is too politically biased, so you base it on estimates done by your favorite interest group? Once passed, do you consider the time composition of the resulting debt issued by Treasury, figuring you'll have to pay your share of each debt instrument as it matures; or do you assume Treasury will simply roll some of it over? If so, what is the rational estimate of how much? Now, presumably you base your share of this cost on actuarial tables indicating how much time you have left, right? Do you make adjustments based on hereditary and lifestyle factors? If so, how much? Finally, it's possible Congress might in the future choose to stick some of the resulting tax burden on to some other economic class, leaving you off the hook; or the opposite might happen. How does our rational actor judge this?

"Personally, I have never mapped out my preferences, or used calculus when I go shopping. So what?"

If your claim is that individuals adjust their behaviour in response to government budgets such that Ricardian equivalence holds, I would like to see some evidence.

Moreover, you argue that people who disagree with you on this are essentially treating people like idiots. I don't know if you have other arguments back there in reserve, but this is obviously totally irrelevant. This isn't Sunday school.

"Personally, I have never mapped out my preferences, or used calculus when I go shopping. So what?"

So, you've admitted that you're not a rational shopper. Most people are not. That's a well known fact an is used by many forms of advertising that encourage people to buy some stuff they don't need. So why are you arguing that it's OK to treat people as rational macroeconomic agents while admitting that you don't rationalize your own shopping?

I'm not sure how we got from debt constraints to a discussion of rationality in economics, but what the heck. Rationality says no more than that economic agents have well-defined objective functions and constraints, and that they optimize. This permits essentially anything, but it is very useful as it imposes some scientific discipline on how we do economics. Rationality certainly does not mean that everyone knows everything. I'm quite fond of writing down models in which economic agents face severe constraints on their information sets, and where acquiring more information can be costly. That's how we explain phenomena like monetary exchange and banking.

Now, the immediate issue here seems to be Ricardian equivalence. What I teach my students is that Ricardian equivalence is a very useful starting point for understanding some elements of fiscal policy. At the minimum, this gets students to think about the government's intertemporal budget constraint, which is a fact of life - a government deficit is clearly just deferred taxation. Then, in class, we start relaxing some of the assumptions that we need to make Ricardian equivalence work - perfect credit markets, no distribution effects (wihin or across generations), lump-sum taxation, etc. You need to be careful about this, as I said above, as in some circumstances, for example credit market frictions, the government has no clear advantage over the private sector. However, we have some clear cases in which government debt matters. One thing that works, for example in New Monetarist Economics, is that you can have a scarcity of liquid assets used in financial trade. If the government runs a deficit and floats more government debt, this can relax financial market constraints, and you can make everyone better off. This is consistent with some of Ricardo Caballero's ideas.

What the second-to-last anonymous is discussing above is not a departure from rationality. These are just information frictions. You can model those things and still be consistent with rationality.

One last point: You need not be afraid of rationality. There is a misconception that goes at least as far back as the 1970s, that rationality leads you down a road to laissez-faire, and that irrationality is somehow the foundation for government intervention. Sometimes Krugman thinks like that. This is false. As Woodford has shown, you can be a hard-core Keynesian and stick to mainstream macroeconomics.

Eggertson and Krugman ignore not just the literature on debt and financial constraints outside the new-keynesian framework (like Mendoza's work, and this might be just plain ignorance), but also papers in the new-keynesian framework that have already done what they do (see for instance here, from a paper by Iacoviello http://ideas.repec.org/a/aea/aecrev/v95y2005i3p739-764.html). What they do might be ok if what they want to do is to sell their stuff to the NYT readers, but if Krugman wants to get back in the research arena, he probably has to do more reading and less writing for some time to come.

Agreed, thanks to anon from tx -- the Seater paper is indeed enlightening, if only as a case study of how groupthink progresses. It spends countless pages on marginally relevant issues like inter-generational dynamics, then exactly one paragraph on the crux of the matter. "Households do not change their consumption when policy changes are announced or could be reasonably anticipated but only when those changes actually occur ..." After two sentences pondering this conundrum, he shrugs his shoulders and moves on. Oh well.

1. The US government appears to be good at collecting taxes and enforcing payment. The Italian government, for example, is not good at it. In southern Italy, the mafia is much better on collecting on its debts than is the government.

I'm confused. Isn't rationality, in the sense of well defined VNM utility functions actually pretty strong? And people test that assumption in the lab all the time.Rationality in the sense of complete and transitive preferences is pretty weak, but expected utility hypothesis is much stronger. (though we don't have a good alternative, so we just work with what we got - but it doesn't mean that assumption is innocuous). ~Larry

"I will not be able to convince you of anything, so I'm not going to waste my time trying."

Well, only the first clause is clearly a prediction. If you add the second clause, there is perhaps an implicit prediction (such as "Even if I wasted my time trying to supply one, then you would still not be convinced"), but it is not clearly one, and allows you the speaker an option as to whether it is really a prediction or not. This is one reason why I wanted to see an actual prediction or predictions spelled out, rather than being airily told to look at your papers. There is a far larger uncertainty as to what is actually a prediction than is supposed. Astrologers use this ambiguity all the time.

In any case you have misunderstood me in my wanting a prediction that convinces me. What I want is a prediction now about the future. So I can't be convinced now, only in the future, should the prediction turn out correct.

Why do I want this kind? Well, you have probably made predictions in the past about the present which have turned out true. And you have also probably made predictions in the past about the present which have turned out false. You may well even have used the same model to make both the true and the false predictions. So your ability to be selective - choosing only the predictions that turned out well - does not in any way enhance my ability to decide whether your models are really turning out true predictions. On the other hand, making a prediction now about the future, and labelling it as a prediction, takes away your chance to be selective. Obviously, we can all make predictions that will turn out true; I predict the US unemployment rate will be higher than 8% next month. It will turn out true - big deal. We can also always make ambiguous predictions; this is often done because of ambiguity about the actual threshold and the timing, e.g. "inflation will stay low for some time." I think that's a pretty safe prediction, not because I think that inflation *will* stay low for some time, but because inflation will stay low for enough time such that, even if inflation does shoot higher, one can always re-interpret "low" and "some time" favorably so that the prediction, in fact, turns out correctly.

All this to say that I think the prediction you gave (in the first clause) is true, but your implicit prediction is false. You will not be able to convince me, precisely because you have not tried. On the other hand, if you actually tried, and you actually came up with a good prediction (e.g. "US headline inflation will be 10% in 1 year"), then I would be more convinced than not.

What you are talking about is forecasting. For that I don't need any economics. Statistics will do. Predicting the effects of changes in policy is another matter. That's where we have to get serious about economic theory. I'll give you a prediction about the effects of policy, based on what I know. Within a year, we will have inflation greater than the Fed's implicit inflation target of 2%. Come back in a year (November 27, 2011). If I'm wrong, I'll explain why.

Government taxing power is qualitatively different from the legal -or illegal-power of a private indvidual to collect debt.

A private individuals can size assets (at a loss) of the private individual who signed the contract (depending on the kind and degree of liability which depends on the contract).

The government collects future taxes on a multitude of individuals which have future income and/or wealth. Sure, the government get zero from those who have no income or no wealth. But as long as someone has income and wealth and he/she will pay taxes, the government has taxing power.

Among the most absurd assumption of inter-temporal optimization is that I can be sure that I will pay taxes in the future. How do you know? Sure, if you are a professor at Harvard, eventually you can be quite sure, but entrepreneurs and workers don't know whether and how much they will pay to the government in the future because they take risky decisions.

From the point of view of the government, who cares who's gonna pay taxes in the future. Basically, the government signs contracts in the future from those who can pay, will take the money from them immediately on the promise to sell goods in the next future and can eventually decide to revise its decisions and give the goods to someone else or give no good at all.

Consequently, once the real world where you and I live shows that the government has a clear advantage over the private sector (something a two-year old baby intuitively grasps), we can flush the Ricardian equivalence and strat to talk like human beings.

Your problem is, however, much deeper: you use mathematics to make ideology. But in the process, you loose contact with the real world. My rule: I take an economist seriously only if he/she stops to talk about Keynesianism vs. Positivism. Grow up, man!

"Imagine a pure endowment economy in which no aggregate saving or investment is possible, but in which individuals can lend to or borrow from each other. Suppose, also, that while individuals all receive the same endowments, they differ in their rates of time preference. In that case, “impatient” individuals will borrow from “patient” individuals. We will assume, however, that there is a limit on the amount of debt any individual can run up. Implicitly, we think of this limit as being the result of some kind of incentive constraint; however, for the purposes of this paper we take the debt limit as exogenous. Specifically, assume for simplicity that there are only two representative agents, each of whom gets a constant endowment (1/2)Y each period."

It looks as if they were modeling a lost episode of Star Trek. No wonder they end up with aggregate demand curves that have the same signed (positive) slope as aggregate supply curves. Topsey-turvey economics, indeed.

Hi together. At the moment I am reading the paper "Debt, Deleveraging and the Liquidity Trap". I have some problems with linearizing the first equation (demand side, borrower equation). It would be great if anyone of you could give me a hint :)